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We give a lattice-theoretic classification of non-symplectic automorphisms of prime order of irreducible holomorphic symplectic manifolds of   $\operatorname{OG10}$   type. We determine which automorphisms are induced by a non-symplectic automorphism of prime order of a cubic fourfold on the associated Laza–Saccà–Voisin manifolds, giving a geometric and lattice-theoretic description of the algebraic and transcendental lattices of the cubic fourfold. As an application we discuss the rationality conjecture for a general cubic fourfold with a non-symplectic automorphism of prime order.

Non-symplectic Automorphisms of Prime Order of O’Grady’s Tenfolds and Cubic Fourfolds